This is a good post, and will be helpful to a lot of folks!

Below are some comments for future posts.

You x- and y-axes would benefit from some labels.

A log-log plot would also be helpful here, as it will reign in the crazy differences in scale on the opposite sides of the graph.

You also don't really need to simulate: each card has a well-defined probability mass function, and the sum of PMFs is pretty straightforward.